The comprehension of object relative clauses and objects WH-questions in Brazilian Portuguese is investigated. Being the processing of these sentences highly costly, it causes comprehension difficulties, especially for SLI children. Processing cost is characterized on the basis of an integrated model of on-line linguistic computation, incorporating minimalist assumptions. The working hypothesis is that the processing cost of such structures can be differentiated as a function of the type of features of the elements involved in the syntactic computation, and the possibility of the immediate mapping of DPs onto background information. An element of the same kind of the moved constituent, when situated between the canonical and the final position of the latter, would lead to high processing cost, in the light of the Extended Relativized Minimality Principle. It was then predicted that the presence of an intervening pronominal DP would facilitate comprehension. Moreover, the possibility was considered of an intervening element to allow the anticipation of a verb/object relation before the object position was found and the antecedent reactivated, thereby facilitating processing. 71 children (aged 7–10) were tested by means of MABILIN. An experiment aiming at verifying those predictions was conducted with 20 children identified as language impaired and 20 typically developing children. A significant improvement in performance could be attested when the intervening element was a pronominal DP, particularly in the SLI group, and when integration with background information was possible. Reading material to children with language difficulties is presented, which is based on these results.